I am not an expert. I will try to explain in a non-expert's language.

HIP check, I believe is, Higher Intermediate Point check.

It has to do with stopovers. Say if you fly from X to Y, you could route it via any points between X and Y provided the MPM is within limits. Say, if you want to fly from X to A to B to Y, and stop at A. And if the fare from A to Y is higher than your X to Y fare, and if there is HIP check in the fare rule, you will be required to pay the fare difference. But if there is no HIP check in the fare rule, then you can stop anywhere you like without having to worry about the fares ex the stopover points.

If there are anybody more knowledgeable than myself, please feel free to elaborate.